%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : KLE113+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n009.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 07:44:20 AM UTC 2026
% Result : Theorem 0.14s 0.39s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 9
% Syntax : Number of formulae : 36 ( 36 unt; 0 def)
% Number of atoms : 36 ( 35 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 12 ( 12 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 3 ( 2 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-2 aty)
% Number of variables : 25 ( 1 sgn 12 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(additive_commutativity,axiom,
! [A,B] : addition(A,B) = addition(B,A),
file('theBenchmark.p',additive_commutativity) ).
fof(additive_identity,axiom,
! [A] : addition(A,zero) = A,
file('theBenchmark.p',additive_identity) ).
fof(multiplicative_right_identity,axiom,
! [A] : multiplication(A,one) = A,
file('theBenchmark.p',multiplicative_right_identity) ).
fof(right_annihilation,axiom,
! [A] : multiplication(A,zero) = zero,
file('theBenchmark.p',right_annihilation) ).
fof(domain1,axiom,
! [X0] : multiplication(antidomain(X0),X0) = zero,
file('theBenchmark.p',domain1) ).
fof(domain3,axiom,
! [X0] : addition(antidomain(antidomain(X0)),antidomain(X0)) = one,
file('theBenchmark.p',domain3) ).
fof(domain4,axiom,
! [X0] : domain(X0) = antidomain(antidomain(X0)),
file('theBenchmark.p',domain4) ).
fof(forward_diamond,axiom,
! [X0,X1] : forward_diamond(X0,X1) = domain(multiplication(X0,domain(X1))),
file('theBenchmark.p',forward_diamond) ).
fof(goals,conjecture,
! [X0] : forward_diamond(X0,zero) = zero,
file('theBenchmark.p',goals) ).
fof(goals_neg,negated_conjecture,
~ ! [X0] : forward_diamond(X0,zero) = zero,
inference(assume_negation,[status(cth)],[goals]) ).
fof(nnf_27,plain,
? [X0] : forward_diamond(X0,zero) != zero,
inference(fof_nnf,[status(thm)],[goals_neg]) ).
fof(sk_goals_neg,plain,
forward_diamond(sK0,zero) != zero,
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[nnf_27]) ).
cnf(c_30,negated_conjecture,
forward_diamond(sK0,zero) != zero,
inference(split_conjunct,[status(thm)],[sk_goals_neg]) ).
cnf(c_34,plain,
forward_diamond(A,B) = domain(multiplication(A,domain(B))),
inference(clausify,[status(thm)],[forward_diamond]) ).
cnf(c_42,plain,
domain(A) = antidomain(antidomain(A)),
inference(clausify,[status(thm)],[domain4]) ).
cnf(c_43,plain,
addition(antidomain(antidomain(A)),antidomain(A)) = one,
inference(clausify,[status(thm)],[domain3]) ).
cnf(c_46,plain,
multiplication(antidomain(A),A) = zero,
inference(clausify,[status(thm)],[domain1]) ).
cnf(c_48,plain,
multiplication(A,zero) = zero,
inference(clausify,[status(thm)],[right_annihilation]) ).
cnf(c_54,plain,
multiplication(A,one) = A,
inference(clausify,[status(thm)],[multiplicative_right_identity]) ).
cnf(c_57,plain,
addition(A,zero) = A,
inference(clausify,[status(thm)],[additive_identity]) ).
cnf(c_59,plain,
addition(A,B) = addition(B,A),
inference(clausify,[status(thm)],[additive_commutativity]) ).
cnf(c_149,negated_conjecture,
domain(multiplication(sK0,domain(zero))) != zero,
inference(paramod,[status(thm)],[c_34,c_30]) ).
cnf(c_150,negated_conjecture,
domain(multiplication(sK0,antidomain(antidomain(zero)))) != zero,
inference(paramod,[status(thm)],[c_42,c_149]) ).
cnf(c_62,negated_conjecture,
antidomain(antidomain(multiplication(sK0,antidomain(antidomain(zero))))) != zero,
inference(paramod,[status(thm)],[c_42,c_150]) ).
cnf(c_67,plain,
addition(antidomain(A),antidomain(antidomain(A))) = one,
inference(paramod,[status(thm)],[c_59,c_43]) ).
cnf(c_101,plain,
antidomain(one) = zero,
inference(paramod,[status(thm)],[c_54,c_46]) ).
cnf(c_123,plain,
addition(zero,A) = A,
inference(paramod,[status(thm)],[c_59,c_57]) ).
cnf(c_151,plain,
addition(zero,antidomain(antidomain(one))) = one,
inference(paramod,[status(thm)],[c_101,c_67]) ).
cnf(c_152,plain,
addition(zero,antidomain(zero)) = one,
inference(paramod,[status(thm)],[c_101,c_151]) ).
cnf(c_142,plain,
antidomain(zero) = one,
inference(paramod,[status(thm)],[c_123,c_152]) ).
cnf(c_153,negated_conjecture,
antidomain(antidomain(multiplication(sK0,antidomain(one)))) != zero,
inference(paramod,[status(thm)],[c_142,c_62]) ).
cnf(c_154,negated_conjecture,
antidomain(antidomain(multiplication(sK0,zero))) != zero,
inference(paramod,[status(thm)],[c_101,c_153]) ).
cnf(c_155,negated_conjecture,
antidomain(antidomain(zero)) != zero,
inference(paramod,[status(thm)],[c_48,c_154]) ).
cnf(c_156,negated_conjecture,
antidomain(one) != zero,
inference(paramod,[status(thm)],[c_142,c_155]) ).
cnf(c_157,negated_conjecture,
zero != zero,
inference(paramod,[status(thm)],[c_101,c_156]) ).
cnf(c_148,negated_conjecture,
$false,
inference(copy,[status(thm)],[c_157]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE113+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n009.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Fri Sep 25 19:23:43 UTC 2026
% 0.14/0.36 % CPUTime :
% 0.14/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.14/0.36 % Process 2308153 was started by sandbox2 on n009,
% 0.14/0.36 % Fri Sep 25 19:23:43 2026
% 0.14/0.36 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.14/0.37
% 0.14/0.37 % From the command line: assign(max_seconds, 300).
% 0.14/0.39
% 0.14/0.39 % SZS status Theorem for theBenchmark
% 0.14/0.39
% 0.14/0.39 % Proof 1 at 0.01 (+ 0.00) seconds.
% 0.14/0.39 % Length of proof is 24.
% 0.14/0.39 % Level of proof is 4.
% 0.14/0.39 % Maximum clause weight is 49.000.
% 0.14/0.39 % Given clauses 31.
% 0.14/0.39
% 0.14/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------